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Lesson Example Discussion Quiz: Class Homework

Lesson

Title: Multiplication theorem for Independent Events

Grade: 9-a Lesson: S3-L4

Explanation: Hello students, let us learn a new topic in statistics today with definitions, concepts, examples, and worksheets included.

Lesson:

Definition: Multiplication theorem for Independent Events:

The multiplication rule of probability explains the condition between two events.
If A and B are two independent events,then the product of the simultaneous occurence is equal to the product of their individual probabilities.

i.e, P (A ∩ B) = P(A) P(B)

Independent Events: Event are said to be independent if the happening of one event does not depend upon happening or non-happening of the other events.

$1$

Explanation:

Let \$m_1\$ be the number of favourable cases to the happening of the event A out of \$n_1\$ exhaustive and equally likely cases

⇒ P(A) = \$m_1/n_1\$

Let \$m_2\$ be the number of favourable cases to the happening of the event B out of \$n_2\$ exhaustive and equally likely cases

⇒ P(B) = \$m_2/n_2\$

Now, by the fundamental principle of counting,the number of favourable cases to the happening of the event A and B is \$m_1,m_2\$ ouot of \$n_1,n_2\$

⇒ P(A ∩ B) = \$(m_1m_2)/(n_1n_2)\$

⇒ P(A ∩ B) = \$(m_1/n_1)(m_2/n_2)\$

⇒ P(A ∩ B) = P(A) P(B)